Given:

$\displaystyle 2x^2y'' + 3xy' + (2x^2 - 1)y = 0$

Question:

Find the indicial equation and determine the two singular roots.

I know how to solve it when the equation is of the form:

$\displaystyle x^2y'' + \alpha xy' + \beta y$

However here, $\displaystyle \beta = 2x^2 - 1$ and is not a constant. How am I supposed to find the indicial/characteristic equation here?

In the solutions, they just ignore the $\displaystyle 2x^2$ factor and proceed as if the equation was $\displaystyle 2x^2y'' + 3xy' - y = 0$. I just don't understand how the $\displaystyle 2x^2$ factor can be ignored.

Any suggestions?